In abstract visual reasoning, monolithic deep learning models suffer from limited interpretability and generalization, while existing neuro-symbolic approaches fall short in capturing the diversity and systematicity of attributes and relation representations. To address these challenges, we propose a Systematic Abductive Reasoning model with diverse relation representations (Rel-SAR) in Vector-symbolic Architecture (VSA) to solve Raven's Progressive Matrices (RPM). To derive attribute representations with symbolic reasoning potential, we introduce not only various types of atomic vectors that represent numeric, periodic and logical semantics, but also the structured high-dimentional representation (SHDR) for the overall Grid component. For systematic reasoning, we propose novel numerical and logical relation functions and perform rule abduction and execution in a unified framework that integrates these relation representations. Experimental results demonstrate that Rel-SAR achieves significant improvement on RPM tasks and exhibits robust out-of-distribution generalization. Rel-SAR leverages the synergy between HD attribute representations and symbolic reasoning to achieve systematic abductive reasoning with both interpretable and computable semantics.

We revisit the recently introduced Local Glivenko-Cantelli setting, which studies distribution-dependent uniform convegence rates of the Maximum Likelihood Estimator (MLE). In this work, we investigate generalizations of this setting where arbitrary estimators are allowed rather than just the MLE. Can a strictly larger class of measures be learned? Can better risk decay rates be obtained? We provide exhaustive answers to these questions -- which are both negative, provided the learner is barred from exploiting some infinite-dimensional pathologies. On the other hand, allowing such exploits does lead to a strictly larger class of learnable measures.

A metric tensor for Riemann manifold Monte Carlo particularly suited for non-linear Bayesian hierarchical models is proposed. The metric tensor is built from symmetric positive semidefinite log-density gradient covariance (LGC) matrices, which are also proposed and further explored here. The LGCs generalize the Fisher information matrix by measuring the joint information content and dependence structure of both a random variable and the parameters of said variable. Consequently, positive definite Fisher/LGC-based metric tensors may be constructed not only from the observation likelihoods as is current practice, but also from arbitrarily complicated non-linear prior/latent variable structures, provided the LGC may be derived for each conditional distribution used to construct said structures. The proposed methodology is highly automatic and allows for exploitation of any sparsity associated with the model in question. When implemented in conjunction with a Riemann manifold variant of the recently proposed numerical generalized randomized Hamiltonian Monte Carlo processes, the proposed methodology is highly competitive, in particular for the more challenging target distributions associated with Bayesian hierarchical models.

Activation functions play a significant role in neural network design by enabling non-linearity. The choice of activation function was previously shown to influence the properties of the resulting loss landscape. Understanding the relationship between activation functions and loss landscape properties is important for neural architecture and training algorithm design. This study empirically investigates neural network loss landscapes associated with hyperbolic tangent, rectified linear unit, and exponential linear unit activation functions. Rectified linear unit is shown to yield the most convex loss landscape, and exponential linear unit is shown to yield the least flat loss landscape, and to exhibit superior generalisation performance. The presence of wide and narrow valleys in the loss landscape is established for all activation functions, and the narrow valleys are shown to correlate with saturated neurons and implicitly regularised network configurations.

A fundamental issue for federated learning (FL) is how to achieve optimal model performance under highly dynamic communication environments. This issue can be alleviated by the fact that modern edge devices usually can connect to the edge FL server via multiple communication channels (e.g., 4G, LTE and 5G). However, having an edge device send copies of local models to the FL server along multiple channels is redundant, time-consuming, and would waste resources (e.g., bandwidth, battery life and monetary cost). In this paper, motivated by the layered coding techniques in video streaming, we propose a novel FL framework called layered gradient compression (LGC). Specifically, in LGC, local gradients from a device is coded into several layers and each layer is sent to the FL server along a different channel. The FL server aggregates the received layers of local gradients from devices to update the global model, and sends the result back to the devices. We prove the convergence of LGC, and formally define the problem of resource-efficient federated learning with LGC. We then propose a learning based algorithm for each device to dynamically adjust its local computation (i.e., the number of local stochastic descent) and communication decisions (i.e.,the compression level of different layers and the layer to channel mapping) in each iteration. Results from extensive experiments show that using our algorithm, LGC significantly reduces the training time, improves the resource utilization, while achieving a similar accuracy, compared with well-known FL mechanisms.

We present a novel approach to semi-supervised learning which is based on statistical physics. Most of the former work in the field of semi-supervised learning classifies the points by minimizing a certain energy function, which corresponds to a minimal k-way cut solution. In contrast to these methods, we estimate the distribution of classifications, instead of the sole minimal k-way cut, which yields more accurate and robust results. Our approach may be applied to all energy functions used for semi-supervised learning. The method is based on sampling using a Mul-ticanonical Markov chain Monte-Carlo algorithm, and has a straightforward probabilistic interpretation, which allows for soft assignments of points to classes, and also to cope with yet unseen class types. The suggested approach is demonstrated on a toy data set and on two real-life data sets of gene expression.